Super Sampling of Digital Video 22 February ( x ) Ψ

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1 Approved for public release; distribution is unlimited Super Sampling of Digital Video February 999 J. Schuler, D. Scribner, M. Kruer Naval Research Laboratory, Code 5636 Washington, D.C ABSTRACT Certain imaging applications can exploit features beyond the spatial resolution of a sensor through computational super-resolution techniques. One particular method, super-sampling, involves assimilating multiple frames of digital video into composite video frames of higher average sampling density than the original sensor. Under certain conditions of scene motion and sensor characteristics, the effective resolution is significantly enhanced.. Preliminary on Focal Plane Array Image Sampling An ideal scene function ( x x, t) Ψ, describes with limitless detail the radiant intensity of the world relative to camera coordinates. An ideal lens geometrically projects this function onto the focal plane, where [ ] x x s geometric, ( x ) Ψ t, x, t, m m m,m are the magnification factors. In practice, lenses exhibit limited spatial fidelity and the projected optical image is sampled by array of finite sized detectors. The resulting signal is degraded due to the separable effects of lens and pixel to generate a pseudo-image, expressed in the space and spatial frequency domains as s S pseudo pseudo The spatial extent of the photo-detector pixel with dimensions [ a ] the geometric image with impulse response ( x, x, t) = hpixel ( x, x )** h psf ( x, x )* * sgeometric( x, x, t) ( F, F, t) = H ( F, F ) H ( F, F ) S ( F, F, t) pixel psf,a geometric serves as a ''box car'' integrator of h pixel x x ( x, x ) = rect rect a a

2 Form SF98 Citation Data Report Date ("DD MON YYYY") 0999 Title and Subtitle Super Sampling of Digital Video Authors Report Type N/A Dates Covered (from... to) ("DD MON YYYY") Contract or Grant Number Program Element Number Project Number Tas Number Wor Unit Number Performing Organization Name(s) and Address(es) Naval Research Laboratory, Code 5636 Washington, D.C Sponsoring/Monitoring Agency Name(s) and Address(es) Performing Organization Number(s) Monitoring Agency Acronym Monitoring Agency Report Number(s) Distribution/Availability Statement Approved for public release, distribution unlimited Supplementary Notes Abstract Subject Terms Document Classification unclassified Classification of Abstract unclassified Classification of SF98 unclassified Limitation of Abstract unlimited Number of Pages 6

3 The spatial frequency response of such a pixel is the separable function H pixel ( F, F ) = a a sin af ( a F ) sin ( a F ) The lens point spread function can be characterized in the spatial frequency domain as a monotonically decreasing function. Assuming a distortion-less optic, the Modulation Transfer Function (MTF) of a unit-sized pixel in one direction of continuous spatial frequency is graphically presented in Figure. a F Continuous Spatial Frequency Figure Continuous Space MTF of a Unit Sized Pixel Integrating and reading out the photo-detector array with detector pitches [ ] digitizes the pseudo-image, creating a discrete representation [ n, n, n ] = s ( n b, n b n t ) sdigital 3 pseudo, 3 cloc b,b at a cloc rate t cloc The Discrete Space Fourier Transform of the sampled image is a periodic extension of the Continuous Space Fourier Transform of the pseudo-image 3 ( f ) =, f, n3 S pseudo,, n tcloc b b l b b where discrete frequency is related to continuous frequency by f l Sdigital 3 f F f = = Fsample b F The MTF of the same unit sized pixel sampled in a 00% fill factor lattice is graphically presented in Figure for one direction of discreet spatial frequency. Note that the low spatial sampling rate of a FPA introduces significant alias distortion of all but the lowest spatial frequencies.

4 Figure Discrete Space MTF of a 00% Fill Factor FPA Conventionally, spatial resolution is significantly improved by introducing a blurring Nyquist optic to prefilter all spatial frequencies above the sampling fold-over frequencies at ±. Clever alternatives to such a blurring optic is to dither or micro-scan the FPA imaging system to synthetically increase the sampling rate. The MTF that results from a 6-fold reduction in detector pitches b is graphically presented in Figure 3 for one direction of discreet spatial frequency. [ ],b Digital Frequency Digital Frequency Figure 3 Discrete Space MTF of a 00% Fill Factor FPA subject to 6-fold dithering Note that although the pixel blur is enhanced over the domain [,+ ], alias distortion is significantly reduced, permitting restoration by an image-sharpening filter that was inapplicable to the low-resolution image.. Motion Estimation All forms of super-sampling require re-assembly of a temporal cube of digital video into a single image with a higher spatial sampling density 4. The success of such processing hinges on accurate nowledge of the FPA motion relative to the object scene. Initial approaches that incorporated a mechanically controlled dither held hope that the inter-image motion would be a nown uniform shift determined by a commanded position change 5. Disappointingly, empirical results show that a nown-shift model is insufficient to characterize the FPA motion when the sensor platform has additional vibration or translational motion 6. The next iteration is to estimate the true shift by any member of a well-developed class of image displacement estimation algorithms 7. Even still, this is insufficient to characterize the motion for most image sequences acquired from moving platforms 8. As previously reported, we generated very promising results by applying numerous image displacement estimators across the image and fitting

5 the resulting motion field to an affine displacement model characteristic of classical perspective transformations. Current research is exploring wavelet based parametric models 9 to account for higher order terms of the basic perspective transformation to account for simple geometric distortions of the sensor optics. 3. Results We extend our analysis from 8x8 MWIR data of the NRL Threat Warning Program 0 to 640x480 MWIR data of the previously reported SASSY program. We were provided several short (30-50 frame) sequences from an airborne ingress into a collection of targets. For compliance with RS-70 video, a 300x480 window of imagery with a : interlace was digitally recorded. Hence, every FPA integration window alternated between even and odd subsets of the 480 available rows to generate a new 300x40 image. Because of the very limited temporal data, we could not compute a fully meaningful affine optical flow model as previously demonstrated. Instead we utilized a strictly translational displacement model with limited success, and implemented a 5-fold increase in the spatial sampling rate of the video sequence. Figure 4 8x8 window of Data (Left) and subsequent 5-fold Super Sampling (Right)

6 Figure 5 Original Data (Upper Left), Interpolated Imagery (Upper Right) Super Sampled Imagery (Bottom) 4. Conclusion Resolution enhancement through temporal super sampling has been demonstrated on a number of recorded digital video sequences. Most significantly, none of the video sequences involved controlled micro-dither scanning, and no consideration was given for the subsequent resolution enhancement analysis performed years after data acquisition. This underscores the fundamental robustness of the super sampling approach, and suggests an immediate deployment in a prototype real-time system without further need for the development of micro-dithering hardware. D.A. Scribner, M.S. Longmire, M.R. Kruer, Analytic modeling of Staring Infrared Systems with Multidimensional Matched Fitlers, SPIE Vol. 890 Infrared Systems and Components II (988) G.R. Cooper, C.D. McGillem, Modern Communications and Spread Spectrum, McGraw-Hill Inc.(986) 3 J.G. Proais, D.G. Manolais, Digital Signal Processing Principles, Algorithms, and Applications, Macmillan Publishing Company (99)

7 4 J.M. Schuler, D.A. Scribner, M.R. Kruer, Super Resolution Imagery from Multi-Frame Sequences with Random Motion Proceedings on the 998 Meeting of the IRIS Specialty Group on Passive Sensors Vol. (998) 5 W.F. O Neal Experimental Performance of a Dither-Scanned InSb Array Proceedings on the 993 Meeting of the IRIS Specialty Group on Passive Sensors (993) 6 S. Cain, E. Armstrong, B. Yasuda Joint Estimation of Image, Shifts, and NonUniformities from IR Images Proceedings on the 997 Meeting of the IRIS Specialty Group on Passive Sensors Vol. (997) 7 A. Schaum, M. McHugh, Analytic Methods of Image Registration: Displacement Estimation and Resampling, NRL Report 998 U.S. Naval Research Laboratory, Washington, DC (99) 8 Q. Zheng, R. Chellappa A Computational Vision Approach to Image Registration Tech. Rep. CAR-TR-583 Center for Automation Research, University of Maryland (99) 9 J. Magerey, N. Kingsbury Motion Estimation Using a Complex-Valued Wavelet Transform IEEE Transactions on Signal Processing Vol. 46, No4 (April 998) 0 K. Saredy et. al. Performance Evaluation of a Staring Two Color Missile Approach Warning Sensor Proceedings of the 995 IRIS Specialty Group on Passive Sensors (995) S.B. Campana, B. Haugh, J.Toner, L. McMichael Results of Airborne Tests of a Medium Wavelength Infrared Imager Proceedings of the 996 Meeting of the IRIS Specialty Group on Passive Sensors (996)